II. The energy spectrum of ejected atoms during the high energy sputtering of gold

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Abstract
Using the technique described in part I, the energy spectrum of sputtered atoms has been determined for several gold specimens, both single crystals and polycrystalline aggregates. The ⟨110⟩, ⟨110⟩ and ⟨121⟩ directions of ejection were chosen for the experiments. Bombardment was with either 43 kev A+ ions, 43 kev Xe+ ions or 66 kev Xe+ ions. The energies of the ejected atoms ranged from some 10−2 ev up to about 104 ev. A peak was generally observed in the energy spectrum between 1 and 10 ev. On the high energy side of this peak the spectrum behaved roughly like E −2, though there were significant deviations from this, particularly for ⟨100⟩ ejection. A theoretical model is developed in which ejection results principally from the generation of atomic collision cascades by the bombarding ion. The assumptions that energy in the cascades is shared by two-body collisions and that the mean collision free path is independent of energy lead to an E −2 spectrum and this prediction should hold roughly from 10 to 103 ev. It is shown that the consequence of surface binding of atoms, with a binding energy E b, is a refraction of atomic trajectories and a peak in the spectrum near E = E b. This random cascade model is unable to explain all features of the spectra, particularly the sharp peaks that appear when they are plotted as time-of-flight spectra. But a more advanced model, which allows for the generation of focused collision sequences by the cascade, fits the data extremely well. This allows for both types of sequence, assisted and simple, and represents their separate characteristics realistically. Deviations from the predictions of the advanced model are confined to energies below 1 ev, where thermal spikes are thought to contribute, and above 103 ev. where the collision free path is probably enhanced by channelling and the normal decrease in cross section with energy. At room temperature the discrepancy only amounts to about 10% of the total sputtering yield. The random cascade and focused collision sequences contribute roughly equal amounts. From a comparison of the predicted and observed spectra it can be deduced, firstly, that for simple focused collision sequences travelling along the ⟨110⟩ rows the maximum energy of propagation is 167±25 ev and their maximum range is at least 21 collisions; secondly, that for ⟨110⟩ assisted sequences the energy limit is 500±100 ev and the maximum range is about 23 collisions: thirdly, that the effective binding energy to the gold surface in these experiments varied from 2·5 to 4·1 ev. An interatomic potential for Au is deduced, consistent with the observed ⟨110⟩ focusing energy and the bulk modulus of elasticity. In the Born–Mayer form. A exp(—r/b), the constants are A = 200±60 kev and b = 2 ·88/(14 ·3 ·0 ·4) Å, valid from 1 ·4 to 2 ·88 Å.